ModellingAssign4
library("readxl")
mydata <- read_excel("wine.xlsx")
mydata## # A tibble: 12,795 x 17
## INDEX Purchase Cases STARS FixedAcidity VolatileAcidity CitricAcid
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 1 3 2 3.2 1.16 -0.98
## 2 2 1 3 3 4.5 0.16 -0.81
## 3 4 1 5 3 7.1 2.64 -0.88
## 4 5 1 3 1 5.7 0.385 0.04
## 5 6 1 4 2 8 0.33 -1.26
## 6 7 0 0 NA 11.3 0.32 0.59
## 7 8 0 0 NA 7.7 0.290 -0.4
## 8 11 1 4 3 6.5 -1.22 0.34
## 9 12 1 3 NA 14.8 0.27 1.05
## 10 13 1 6 4 5.5 -0.22 0.39
## # … with 12,785 more rows, and 10 more variables: ResidualSugar <dbl>,
## # Chlorides <dbl>, FreeSulfurDioxide <dbl>, TotalSulfurDioxide <dbl>,
## # Density <dbl>, pH <dbl>, Sulphates <dbl>, Alcohol <dbl>, LabelAppeal <dbl>,
## # AcidIndex <dbl>TASK 1: EXPLORATORY DATA ANALYSIS and DATA PREP
summary(mydata$Alcohol)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## -4.70 9.00 10.40 10.49 12.40 26.50 653hist(mydata$Alcohol)
mydata <- mydata[mydata$Alcohol >= 0, ]
hist(mydata$Alcohol)
mydata## # A tibble: 12,677 x 17
## INDEX Purchase Cases STARS FixedAcidity VolatileAcidity CitricAcid
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 1 1 3 2 3.2 1.16 -0.98
## 2 NA NA NA NA NA NA NA
## 3 4 1 5 3 7.1 2.64 -0.88
## 4 5 1 3 1 5.7 0.385 0.04
## 5 6 1 4 2 8 0.33 -1.26
## 6 7 0 0 NA 11.3 0.32 0.59
## 7 8 0 0 NA 7.7 0.290 -0.4
## 8 11 1 4 3 6.5 -1.22 0.34
## 9 12 1 3 NA 14.8 0.27 1.05
## 10 13 1 6 4 5.5 -0.22 0.39
## # … with 12,667 more rows, and 10 more variables: ResidualSugar <dbl>,
## # Chlorides <dbl>, FreeSulfurDioxide <dbl>, TotalSulfurDioxide <dbl>,
## # Density <dbl>, pH <dbl>, Sulphates <dbl>, Alcohol <dbl>, LabelAppeal <dbl>,
## # AcidIndex <dbl>Explanation: I removed the negative and zero Alcohol values as those appeared to be errors in the dat. Wine should not have a negative alcohol value.
summary(mydata$Chlorides)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## -1.1710 -0.0320 0.0460 0.0543 0.1520 1.3510 1250plot(mydata$Chlorides)
hist(mydata$Chlorides)
summary(mydata$VolatileAcidity)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## -2.7900 0.1300 0.2800 0.3253 0.6350 3.6800 653plot(mydata$VolatileAcidity)
hist(mydata$VolatileAcidity)
plot(mydata$VolatileAcidity,mydata$Chlorides)
summary(mydata$CitricAcid)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## -3.2400 0.0300 0.3100 0.3101 0.5800 3.8600 653plot(mydata$CitricAcid)
hist(mydata$CitricAcid)
summary(mydata$ResidualSugar)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## -127.800 -1.900 3.900 5.471 16.000 141.150 1224plot(mydata$ResidualSugar)
hist(mydata$ResidualSugar)
summary(mydata$FreeSulfurDioxide)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## -555.00 -1.00 30.00 30.68 70.00 623.00 1263plot(mydata$FreeSulfurDioxide)
hist(mydata$FreeSulfurDioxide)
summary(mydata$Density)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.8881 0.9878 0.9945 0.9943 1.0008 1.0992 653plot(mydata$Density)
hist(mydata$Density)
summary(mydata$TotalSulfurDioxide)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## -823.0 28.0 124.0 121.3 208.0 1057.0 1290plot(mydata$TotalSulfurDioxide)
hist(mydata$TotalSulfurDioxide)
summary(mydata$pH)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.480 2.960 3.200 3.206 3.470 6.130 1022plot(mydata$pH)
hist(mydata$pH)
summary(mydata$Sulphates)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## -3.1300 0.2800 0.5000 0.5262 0.8500 4.2400 1794plot(mydata$Sulphates)
hist(mydata$Sulphates)
summary(mydata$AcidIndex)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 4.000 7.000 8.000 7.769 8.000 17.000 653plot(mydata$AcidIndex)
hist(mydata$AcidIndex)
mydata=abs(mydata)
summary(mydata$Sulphates)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.0000 0.4300 0.5900 0.8462 1.0900 4.2400 1794plot(mydata$Sulphates)
hist(mydata$Sulphates)
mydata$STARS[is.na(mydata$STARS)]=0
mydata$Purchase[is.na(mydata$Purchase)]=0
mydata$STARS## [1] 2 0 3 1 2 0 0 3 0 4 1 2 2 3 0 0 0 3 2 2 1 1 1 0 2 0 2 4 2 1 3 1 0 1 1 2
## [37] 0 2 1 0 2 2 1 1 2 4 1 1 2 0 0 2 1 0 1 0 0 2 1 0 0 3 1 1 1 4 3 0 3 3 1 4
## [73] 0 1 1 1 1 0 1 3 0 0 3 3 0 2 3 1 3 0 0 1 0 1 0 3 1 2 0 1 2 0 3 2 1 2 0 1
## [109] 2 2 0 0 0 2 0 2 1 0 0 1 2 1 2 2 0 1 2 1 0 3 0 3 3 0 0 0 4 2 0 3 0 2 1 1
## [145] 0 3 1 4 3 2 2 0 0 2 2 1 3 0 0 3 2 4 3 0 3 4 0 0 1 0 1 1 2 1 2 0 0 0 3 4
## [181] 2 2 0 1 3 3 3 0 1 0 3 0 0 3 0 2 0 2 3 0 2 3 2 2 3 2 1 2 0 2 1 2 0 2 0 2
## [217] 0 3 1 2 3 0 2 2 1 1 1 3 2 3 0 3 0 0 0 0 0 0 0 3 1 4 3 3 2 4 0 0 2 2 4 1
## [253] 0 3 2 3 2 3 2 2 3 3 1 0 0 3 3 3 0 2 0 2 4 2 2 2 3 3 1 0 0 2 0 2 0 3 1 0
## [289] 0 3 0 0 2 1 0 1 0 0 3 0 2 3 1 0 4 3 2 0 2 3 0 1 2 0 2 2 2 3 0 1 1 0 1 0
## [325] 2 1 3 0 0 2 1 2 0 1 2 3 3 0 2 1 0 2 1 4 0 3 1 3 3 3 3 0 0 1 2 3 0 1 1 1
## [361] 2 1 2 1 3 1 3 2 1 0 2 0 0 1 0 1 2 0 1 0 2 3 2 0 1 1 1 0 3 2 0 2 3 2 0 2
## [397] 0 0 4 0 3 2 1 0 4 2 0 0 1 0 2 0 0 1 3 0 3 2 3 1 1 0 1 0 2 0 1 1 2 0 2 0
## [433] 2 2 1 1 0 3 2 0 1 2 3 2 1 4 2 2 0 2 0 2 0 1 3 0 0 0 2 3 0 1 4 0 0 0 0 0
## [469] 0 3 1 3 2 2 2 0 1 0 0 1 0 1 1 0 2 0 2 1 2 0 0 4 4 1 0 1 2 0 1 1 2 2 1 1
## [505] 1 2 2 3 3 0 2 1 1 0 0 2 0 0 0 2 0 3 0 2 0 0 0 0 2 3 1 2 3 3 0 0 2 2 0 4
## [541] 3 2 2 2 0 1 2 3 1 0 0 0 2 4 2 0 0 3 1 2 0 1 0 0 1 0 0 2 1 3 0 0 1 0 1 2
## [577] 2 0 2 1 0 0 3 3 0 3 1 3 0 0 3 1 4 1 2 3 4 1 0 2 0 0 3 3 1 0 2 0 1 1 2 2
## [613] 3 3 3 2 2 0 1 2 2 1 2 0 1 0 4 0 0 2 4 2 2 1 0 4 0 3 2 3 1 0 2 1 1 0 3 1
## [649] 1 2 2 3 1 2 3 1 4 1 2 1 3 1 1 2 1 1 0 0 0 0 3 0 3 1 0 1 3 2 1 4 0 1 2 0
## [685] 1 2 0 0 3 0 0 0 1 1 1 2 1 0 0 2 0 4 3 1 4 3 1 0 1 2 3 4 2 3 1 0 0 4 1 0
## [721] 2 2 1 1 3 1 2 0 2 3 2 3 3 1 0 0 3 0 2 0 1 3 1 0 2 0 1 3 1 2 3 0 4 1 4 0
## [757] 4 0 1 1 1 1 2 3 2 2 2 4 2 0 2 0 2 0 0 0 2 2 2 3 4 1 0 3 3 2 2 0 2 1 2 0
## [793] 2 2 0 3 0 3 2 4 0 1 0 3 1 1 3 2 0 2 2 1 3 0 0 2 1 2 0 1 0 2 1 1 1 4 0 3
## [829] 1 2 4 3 4 1 3 4 1 0 1 0 3 1 2 1 0 0 3 0 1 2 0 3 1 4 0 2 0 0 2 4 4 1 0 0
## [865] 0 2 1 2 0 1 0 0 2 3 2 4 2 2 0 0 2 3 0 2 0 0 2 1 2 2 3 1 1 0 0 3 1 1 4 2
## [901] 3 3 0 0 2 1 2 2 2 3 0 0 0 2 0 0 2 2 2 0 0 0 0 0 0 3 3 3 2 3 0 3 0 1 2 2
## [937] 2 0 0 0 0 0 0 1 0 2 2 1 0 2 2 0 3 2 3 1 2 4 0 1 2 2 0 0 2 1 2 1 0 0 2 0
## [973] 3 4 3 3 2 2 0 0 0 4 1 2 0 2 2 3 3 0 2 0 0 3 2 2 2 2 2 0 3 4 2 0 0 3 2 3
## [1009] 0 2 0 1 0 2 0 2 2 2 2 2 2 1 0 2 4 1 0 0 1 2 0 0 4 0 2 0 0 2 0 2 0 2 1 2
## [1045] 1 0 3 0 2 2 1 1 0 2 2 2 3 1 0 0 2 4 1 2 3 3 0 0 2 0 0 1 3 0 2 1 1 0 3 0
## [1081] 1 1 2 1 0 4 1 1 3 0 1 2 0 4 0 3 0 1 1 1 3 0 1 0 0 0 1 2 0 3 1 2 3 0 0 0
## [1117] 0 0 1 3 3 2 3 4 0 2 1 1 2 2 0 1 0 2 4 0 2 1 2 1 1 0 2 2 0 1 2 4 2 2 0 3
## [1153] 2 0 0 0 2 2 1 2 1 0 2 4 0 2 1 0 2 0 2 3 0 1 2 0 1 0 0 2 2 1 0 2 1 1 0 0
## [1189] 0 0 0 2 3 0 2 4 2 1 0 4 1 3 2 0 0 3 0 2 1 1 0 3 3 3 3 0 4 2 0 2 3 3 2 1
## [1225] 0 3 0 0 1 1 2 4 2 3 2 2 3 0 3 1 0 2 0 3 2 0 1 3 2 0 0 2 2 2 0 2 2 0 2 0
## [1261] 0 1 2 2 3 3 1 1 3 1 0 0 0 0 0 1 1 2 2 1 2 0 1 3 0 3 0 2 3 2 2 0 0 3 0 3
## [1297] 0 0 1 1 2 1 3 2 2 3 0 2 4 4 2 0 2 1 1 3 0 0 2 0 1 1 1 0 2 3 1 0 2 2 2 1
## [1333] 2 2 1 1 1 1 0 0 3 2 1 1 3 2 4 3 0 2 0 0 1 2 2 0 3 3 1 0 0 0 2 2 3 0 0 0
## [1369] 3 1 1 1 0 0 3 2 0 0 1 3 3 2 1 0 4 1 1 1 3 0 0 1 2 2 2 4 2 2 3 0 1 3 2 0
## [1405] 2 2 0 0 2 0 1 1 0 1 2 2 1 1 2 1 3 2 0 0 0 0 2 3 0 0 3 0 0 2 0 0 1 1 1 4
## [1441] 4 0 2 1 4 2 4 3 0 3 0 2 0 3 1 0 0 4 2 3 2 0 2 3 3 4 2 0 0 1 4 4 1 1 0 3
## [1477] 2 3 2 0 2 1 2 1 2 1 0 2 1 0 1 1 1 0 3 1 0 1 3 0 0 0 4 0 1 2 0 0 0 1 2 1
## [1513] 2 4 1 1 2 0 1 0 3 2 1 0 2 1 1 2 0 1 0 3 2 2 0 2 3 2 4 2 1 3 1 2 0 0 3 1
## [1549] 2 3 2 1 1 2 0 0 3 0 3 0 3 0 2 0 3 0 0 2 1 2 1 1 1 3 1 2 4 1 0 2 0 0 1 0
## [1585] 1 1 2 1 1 2 3 2 1 1 1 0 0 0 1 0 2 1 0 0 2 3 1 4 3 1 0 0 3 1 1 2 1 4 1 3
## [1621] 2 0 0 1 1 4 0 0 2 2 0 1 1 3 3 3 2 3 3 2 1 0 3 0 3 0 3 3 2 0 2 1 2 0 2 1
## [1657] 2 2 3 0 3 3 3 2 2 2 2 2 0 0 1 1 1 0 0 0 0 4 1 0 4 0 2 2 3 2 0 2 1 2 1 0
## [1693] 0 3 2 1 3 3 3 0 2 1 3 0 4 3 1 0 0 0 2 2 1 0 2 1 0 2 2 0 1 1 0 2 3 0 0 3
## [1729] 2 0 2 3 3 1 1 0 3 3 1 3 2 1 2 3 1 1 2 2 2 1 3 2 0 2 2 4 3 3 3 0 2 0 0 0
## [1765] 1 4 2 2 3 2 3 2 0 0 0 1 2 3 4 3 0 1 3 2 1 4 2 3 2 2 2 2 1 1 2 1 3 2 2 3
## [1801] 3 3 2 0 1 3 4 1 2 0 2 2 0 3 1 1 3 0 2 1 1 2 2 0 2 0 1 3 2 0 1 2 2 4 2 2
## [1837] 0 1 0 0 0 2 2 2 2 3 1 1 3 1 0 1 1 0 3 0 0 0 4 2 2 1 1 2 1 3 1 0 1 3 2 2
## [1873] 1 4 0 0 0 3 1 3 2 3 2 2 2 4 0 0 3 0 0 1 2 1 3 1 3 0 3 3 1 2 1 2 1 4 0 0
## [1909] 3 1 0 0 0 1 3 1 4 1 2 0 0 0 2 2 0 3 0 2 3 2 4 1 2 1 0 2 2 1 2 1 1 2 0 2
## [1945] 3 2 2 0 2 3 2 2 0 1 0 0 2 3 1 2 1 0 2 1 0 3 0 3 0 0 0 0 0 3 0 1 1 2 1 0
## [1981] 1 3 0 2 3 2 2 0 0 0 1 2 1 0 4 0 2 3 0 0 0 2 1 0 1 2 1 2 0 4 2 0 3 2 2 0
## [2017] 1 1 1 2 3 2 3 0 3 0 1 3 1 0 3 0 3 1 3 1 3 0 2 1 0 3 3 4 4 2 2 1 2 3 0 0
## [2053] 2 2 2 1 0 0 2 0 1 2 0 0 2 3 0 2 2 2 0 0 1 2 0 2 0 0 2 2 1 1 1 3 1 2 1 2
## [2089] 2 3 0 4 0 0 2 0 3 0 1 0 4 0 3 0 2 3 1 2 2 3 3 2 2 0 3 0 0 0 2 3 0 0 0 1
## [2125] 2 1 2 0 2 2 2 2 0 3 3 0 2 3 4 2 1 0 0 3 1 0 0 3 3 4 0 3 0 1 4 1 2 2 1 4
## [2161] 2 1 0 4 0 2 2 4 3 0 1 2 3 2 1 2 3 0 3 0 2 1 0 0 0 2 2 1 0 0 3 2 3 0 3 0
## [2197] 1 1 2 1 0 2 2 4 0 1 0 3 0 2 0 3 2 3 1 4 1 3 2 0 0 1 2 0 3 0 0 0 1 3 3 3
## [2233] 0 2 1 1 2 3 3 1 1 1 2 1 2 0 1 1 0 0 2 2 2 1 0 3 0 1 2 3 1 0 3 1 3 1 2 3
## [2269] 0 2 3 3 2 0 0 0 1 1 2 0 4 2 3 2 1 1 3 2 3 2 1 3 2 0 3 1 2 3 4 1 1 2 1 2
## [2305] 2 1 1 2 2 2 3 1 3 0 0 1 0 2 1 0 3 1 1 3 2 2 3 1 0 2 1 1 2 0 0 2 0 0 2 3
## [2341] 1 2 2 1 2 2 3 2 2 1 1 0 2 2 2 1 2 3 2 4 1 0 1 4 2 4 0 3 2 1 3 0 1 0 2 1
## [2377] 2 0 0 3 2 4 2 0 3 2 2 3 3 0 2 3 2 2 0 1 2 1 3 2 0 0 3 0 3 2 3 2 0 1 3 2
## [2413] 1 1 0 1 0 3 0 2 0 0 1 2 1 1 1 4 2 3 0 0 0 3 0 0 1 0 2 0 0 0 2 3 2 2 0 2
## [2449] 0 3 2 0 0 1 3 3 1 0 0 2 0 0 1 0 0 0 2 3 2 0 2 2 2 2 1 0 0 2 0 1 3 1 3 0
## [2485] 3 2 0 2 3 3 2 2 2 2 2 3 3 0 3 2 4 0 2 2 2 2 0 0 1 0 0 1 1 4 2 1 0 0 1 2
## [2521] 2 0 2 0 2 0 2 2 1 3 1 0 0 0 2 3 0 0 2 0 2 1 3 3 3 2 4 0 0 2 0 0 0 0 1 1
## [2557] 1 2 1 2 2 2 1 1 0 0 0 2 4 0 1 1 0 1 3 1 0 0 3 0 2 0 0 2 0 1 2 0 1 2 2 1
## [2593] 3 1 1 3 2 3 4 3 2 0 4 0 0 0 0 2 0 2 3 2 2 4 1 2 2 0 0 1 2 1 0 1 3 2 0 2
## [2629] 3 3 3 2 2 2 0 1 2 3 3 0 4 0 2 2 2 1 0 2 3 0 2 1 0 1 0 3 2 1 1 2 2 2 3 0
## [2665] 2 0 2 2 2 0 1 1 1 0 0 0 4 3 1 3 0 1 3 3 1 3 2 2 2 0 2 1 0 1 1 3 1 1 0 1
## [2701] 2 0 2 1 2 0 1 2 0 3 2 2 3 1 1 3 3 1 0 0 2 2 3 0 0 3 3 2 3 3 0 2 0 2 2 0
## [2737] 3 1 4 0 1 1 3 1 1 0 2 0 2 0 2 2 3 0 1 4 1 0 0 4 1 0 2 2 2 0 2 2 2 0 2 3
## [2773] 1 0 1 2 2 1 4 4 1 2 2 0 2 3 2 0 2 0 2 3 2 1 2 0 1 2 1 0 4 0 0 3 1 4 1 3
## [2809] 2 2 1 3 1 0 0 1 3 1 2 2 1 2 1 2 1 0 2 1 0 0 1 0 3 2 1 0 1 0 1 3 3 2 0 4
## [2845] 3 2 0 2 0 0 0 0 3 1 2 1 2 0 1 0 0 2 1 2 0 1 0 0 0 3 1 3 1 2 1 2 1 1 1 0
## [2881] 0 2 2 2 2 4 1 1 1 0 0 1 0 2 3 2 2 1 2 0 3 0 4 2 3 2 3 0 2 0 3 3 0 0 1 1
## [2917] 3 0 3 0 2 4 1 0 0 1 2 0 0 0 2 3 1 1 0 2 1 3 0 0 2 3 2 1 3 3 2 0 1 0 2 0
## [2953] 3 1 2 2 2 0 1 2 1 1 3 2 0 1 0 1 0 1 0 3 3 1 1 3 4 2 2 0 0 2 2 0 0 0 1 1
## [2989] 2 0 0 3 1 3 0 4 2 1 1 3 2 1 2 0 4 3 1 0 2 0 0 1 1 0 0 2 2 0 2 0 4 2 3 3
## [3025] 3 2 4 0 2 2 1 1 0 1 3 0 3 0 2 2 3 0 0 0 2 0 0 1 3 4 3 1 2 2 0 3 2 0 2 0
## [3061] 0 2 0 1 0 4 1 0 3 1 0 0 0 1 1 1 0 0 1 3 0 1 2 0 4 1 2 3 0 3 3 2 0 2 2 2
## [3097] 1 2 2 0 2 1 3 0 0 0 2 2 0 2 0 0 3 3 0 3 1 3 1 0 3 2 1 1 1 3 2 3 0 3 2 0
## [3133] 1 2 0 1 4 0 4 0 0 0 1 1 1 1 3 0 2 2 1 0 2 1 1 1 3 1 1 3 0 0 2 2 2 0 3 3
## [3169] 3 1 1 3 1 1 1 0 1 2 0 1 3 2 2 1 1 2 0 2 3 4 3 2 1 0 2 0 3 0 2 3 3 0 1 2
## [3205] 2 2 3 0 4 3 2 4 2 0 2 0 1 4 2 1 2 3 2 3 0 3 4 1 2 0 2 1 1 0 1 2 3 4 2 1
## [3241] 0 2 0 2 1 1 0 0 0 3 1 1 2 2 2 1 0 4 0 2 0 2 1 2 1 2 1 0 3 0 0 2 0 3 1 0
## [3277] 2 0 1 2 2 0 0 1 3 0 2 3 0 2 2 1 2 0 0 1 3 0 0 1 0 1 3 3 2 2 3 0 1 1 0 0
## [3313] 3 2 1 0 2 3 0 3 3 1 1 2 0 2 2 1 0 0 1 2 1 1 4 0 1 0 4 3 2 1 2 2 2 2 4 3
## [3349] 1 0 1 0 2 4 0 1 3 0 0 2 2 1 0 1 1 1 2 2 3 1 0 0 1 0 3 3 2 1 1 4 0 3 3 3
## [3385] 1 0 1 0 4 0 2 0 1 0 0 1 1 0 1 1 1 0 4 0 1 2 1 1 2 1 2 2 0 2 2 2 1 2 1 3
## [3421] 0 2 2 0 2 2 0 0 3 1 1 0 0 1 1 3 1 2 2 2 2 1 2 0 3 2 3 2 3 1 2 2 0 2 3 0
## [3457] 2 2 2 2 1 3 2 0 2 2 2 4 3 2 2 1 1 1 0 1 1 0 2 3 3 1 0 0 0 1 2 3 2 1 2 0
## [3493] 1 2 1 2 2 1 1 0 3 1 3 1 3 1 1 0 2 1 2 1 0 1 2 1 1 0 1 2 3 0 1 0 3 1 4 0
## [3529] 2 2 2 2 0 0 0 3 4 2 0 2 1 0 3 2 0 2 2 3 2 2 3 4 1 1 1 0 4 0 0 1 1 1 0 1
## [3565] 1 0 0 3 4 3 1 3 0 0 1 0 1 3 0 0 0 0 0 0 2 2 2 1 0 0 1 0 1 2 0 0 1 0 2 0
## [3601] 0 2 1 0 0 3 0 2 1 2 0 0 0 3 0 1 1 2 3 0 0 2 2 3 2 0 2 0 4 1 2 2 1 0 0 2
## [3637] 0 1 4 2 2 1 1 2 3 1 3 2 0 1 2 2 0 3 0 0 2 3 2 3 2 2 3 0 1 0 2 0 2 0 1 1
## [3673] 1 0 0 0 2 0 0 2 3 4 0 0 0 3 1 1 3 3 2 1 2 2 2 3 3 3 0 4 3 3 2 2 4 2 0 4
## [3709] 1 0 2 1 1 2 2 0 0 2 0 2 0 2 2 2 0 2 2 0 1 2 1 2 0 1 0 3 2 0 4 0 0 3 1 0
## [3745] 2 2 1 2 4 3 1 1 0 1 2 0 0 3 1 2 2 3 2 1 3 4 3 2 2 1 1 2 1 0 1 1 2 1 0 3
## [3781] 0 2 0 2 1 2 0 0 0 2 3 4 0 0 3 2 3 1 0 3 0 2 2 2 0 2 3 3 1 4 0 0 2 0 3 3
## [3817] 1 1 0 0 2 2 2 2 0 0 1 0 2 0 2 3 2 0 1 3 4 0 4 0 3 1 2 1 3 2 0 2 0 0 0 2
## [3853] 3 2 0 1 2 4 1 0 3 3 1 1 0 3 0 1 2 1 3 4 0 2 1 0 3 2 3 1 2 2 1 0 2 3 0 2
## [3889] 0 0 0 1 1 0 1 1 2 0 3 3 0 1 1 2 0 1 0 2 2 0 2 1 2 2 4 0 2 3 2 3 0 1 4 0
## [3925] 1 0 2 0 0 1 3 1 0 1 2 3 2 0 3 3 1 0 2 1 0 0 3 1 2 1 2 2 1 2 3 0 3 0 1 3
## [3961] 0 0 1 2 2 2 3 1 2 1 1 0 1 1 3 0 1 1 3 2 4 0 2 2 0 0 0 0 0 0 2 2 1 3 3 2
## [3997] 0 0 2 2 1 0 1 2 0 2 1 1 2 0 1 0 0 0 1 0 3 3 1 3 2 1 4 2 4 1 2 0 0 0 2 4
## [4033] 2 0 0 1 1 2 0 4 1 0 3 1 0 0 1 4 1 0 3 2 2 3 2 0 1 0 2 2 1 0 0 2 0 1 0 2
## [4069] 3 1 3 0 2 1 0 0 1 2 0 3 3 0 1 2 3 0 1 2 0 3 3 2 1 1 2 0 0 0 2 3 3 1 0 3
## [4105] 3 3 3 3 1 3 2 3 1 1 0 2 1 2 1 3 0 2 1 3 0 0 3 1 3 3 0 0 4 2 3 2 2 1 1 3
## [4141] 2 0 3 2 3 4 2 1 2 0 2 0 3 2 3 2 0 1 3 2 0 0 0 3 4 0 0 3 1 0 2 2 2 0 0 1
## [4177] 0 2 0 0 2 4 0 0 2 3 2 1 3 0 2 2 0 1 3 1 3 0 1 2 1 3 0 0 3 0 2 0 2 2 3 0
## [4213] 1 0 2 1 4 1 3 3 3 2 3 0 0 0 1 0 3 2 0 1 3 3 2 0 2 3 2 2 0 1 0 1 0 3 2 2
## [4249] 0 0 3 0 1 4 1 2 2 1 0 2 2 2 2 1 3 2 0 2 2 1 3 2 0 1 3 2 3 0 0 2 3 4 1 2
## [4285] 1 2 0 1 1 0 1 2 1 0 0 2 0 0 2 1 2 0 1 1 1 1 1 1 3 2 2 0 3 0 1 2 1 1 1 0
## [4321] 2 0 0 0 3 1 0 1 0 1 1 0 1 0 2 4 0 1 0 1 1 3 3 1 0 1 2 0 0 0 4 2 0 2 0 0
## [4357] 3 1 2 0 2 2 0 2 0 0 0 0 0 0 0 3 3 1 1 1 3 2 1 1 2 3 0 0 2 1 1 2 2 1 0 1
## [4393] 2 0 3 0 2 2 2 3 2 1 3 4 2 0 1 1 2 0 0 1 3 1 1 0 1 1 3 1 4 3 1 2 0 0 2 1
## [4429] 3 2 3 0 1 0 0 3 2 2 3 0 0 0 1 0 1 0 0 1 0 3 1 2 0 0 1 2 0 0 3 0 1 1 1 2
## [4465] 4 3 0 0 0 0 1 0 0 3 0 1 2 1 0 2 0 3 1 3 2 3 2 2 2 2 0 0 3 0 0 3 3 0 2 4
## [4501] 1 3 0 2 2 0 1 3 3 0 1 2 3 2 2 2 2 2 3 1 2 1 4 1 2 0 2 2 3 1 3 1 0 2 1 0
## [4537] 3 2 1 1 0 2 4 3 0 2 3 0 0 1 0 3 3 2 2 3 2 1 3 2 0 4 2 1 1 0 2 1 1 1 0 1
## [4573] 3 2 2 0 0 3 3 2 3 0 2 0 0 0 3 0 3 3 2 2 0 3 0 1 0 3 2 0 1 0 3 1 1 1 2 3
## [4609] 2 1 0 0 0 0 4 0 0 3 3 2 1 2 1 1 4 0 0 1 1 0 1 2 4 2 3 0 1 1 3 2 3 2 3 1
## [4645] 0 1 2 2 0 0 2 0 3 1 1 2 2 2 3 0 0 2 0 0 4 1 3 0 1 1 1 3 0 1 3 1 1 2 2 4
## [4681] 1 2 2 1 2 0 1 2 3 0 0 3 4 1 2 1 2 1 3 2 3 1 3 2 0 4 3 2 0 1 4 0 4 0 0 1
## [4717] 1 4 3 0 3 4 2 3 2 3 1 3 1 1 0 3 2 2 1 0 0 2 2 1 1 0 3 1 4 2 0 4 4 2 1 1
## [4753] 1 0 3 0 2 1 2 0 1 1 0 1 0 2 0 0 1 2 1 1 1 3 3 2 3 1 1 2 3 2 3 0 3 0 0 3
## [4789] 2 1 4 2 0 2 3 0 3 1 0 1 0 0 2 3 0 0 3 1 2 1 2 1 2 0 0 2 3 3 1 2 1 2 1 2
## [4825] 0 0 3 0 2 2 2 1 2 0 1 1 0 3 1 2 1 1 1 1 0 0 0 2 0 2 3 3 3 3 0 2 3 0 4 1
## [4861] 3 0 3 4 0 0 2 1 1 2 0 1 2 1 0 3 1 1 2 0 1 1 2 2 3 3 0 3 2 0 1 0 4 2 2 2
## [4897] 0 0 0 1 0 0 3 1 0 2 0 2 0 3 1 0 2 1 4 4 2 0 0 1 0 3 0 2 1 1 3 2 1 3 3 3
## [4933] 4 0 4 2 0 1 3 1 0 0 3 4 0 3 0 1 2 2 2 2 1 2 3 2 0 0 1 1 0 0 3 3 0 0 0 0
## [4969] 3 4 2 2 2 1 2 3 0 1 1 0 0 3 0 0 2 2 3 1 0 0 1 2 0 1 0 3 3 0 3 1 0 1 0 0
## [5005] 2 3 4 0 0 2 0 1 0 3 2 1 0 3 1 3 0 0 3 0 2 2 0 3 0 0 0 1 1 3 2 2 1 2 0 1
## [5041] 1 1 0 0 3 0 0 0 0 0 1 1 2 0 1 0 2 1 2 1 4 2 2 2 2 1 0 0 1 0 3 2 0 0 2 0
## [5077] 2 3 3 3 0 2 2 2 0 3 1 0 2 2 3 0 2 2 2 2 1 3 3 1 3 0 1 0 0 1 2 1 2 2 2 3
## [5113] 3 3 0 1 0 0 3 0 3 1 2 0 1 1 0 3 2 1 0 0 1 2 0 4 2 1 2 2 4 1 0 0 3 4 4 2
## [5149] 4 3 1 2 0 2 0 1 2 0 2 2 0 3 2 0 4 3 4 0 1 3 1 0 2 3 0 4 3 1 2 0 1 2 1 0
## [5185] 0 3 1 0 0 3 2 3 2 3 3 3 0 1 3 0 3 0 0 2 2 3 3 2 1 3 2 1 2 2 3 2 2 0 2 0
## [5221] 2 3 0 3 3 0 1 2 0 3 0 3 1 1 2 1 2 0 1 4 3 3 3 3 1 1 0 0 3 1 3 1 2 1 3 2
## [5257] 4 1 1 2 4 3 0 2 3 2 3 3 1 2 3 0 2 1 3 0 0 0 3 1 2 2 0 0 3 1 0 1 2 2 2 2
## [5293] 2 2 2 3 0 2 3 4 1 0 1 0 1 0 1 4 4 0 2 2 1 0 3 0 4 1 1 0 0 2 2 0 0 2 0 3
## [5329] 0 0 3 3 0 2 0 2 2 1 0 1 0 3 1 0 0 0 3 2 0 1 0 0 3 3 0 1 2 3 3 0 1 0 2 1
## [5365] 2 3 3 2 2 0 1 1 0 0 2 1 1 3 2 2 2 2 1 2 0 2 1 1 1 3 3 3 3 2 2 0 1 2 4 1
## [5401] 4 0 2 1 2 1 1 0 2 0 2 1 4 0 2 2 4 2 0 1 1 2 2 0 2 0 0 1 2 0 0 2 1 3 0 0
## [5437] 3 3 2 0 0 1 4 4 1 0 3 0 3 2 0 2 0 0 1 4 4 2 3 4 1 1 2 2 2 4 3 0 0 3 1 3
## [5473] 2 3 3 3 2 2 2 1 0 0 2 1 1 3 1 4 0 0 1 1 2 1 0 2 0 0 2 0 0 3 1 2 2 3 3 2
## [5509] 1 0 0 0 1 0 1 2 1 1 2 2 4 2 2 4 3 2 1 3 3 2 0 4 1 3 2 2 2 1 2 1 1 0 2 0
## [5545] 0 3 0 1 2 3 4 1 0 0 0 1 2 3 4 0 3 2 0 0 1 3 0 1 4 0 1 1 2 3 1 1 0 1 1 2
## [5581] 2 1 2 3 3 0 0 3 1 4 2 0 0 1 3 3 2 3 1 1 1 2 3 3 3 3 2 1 4 2 3 1 1 0 3 3
## [5617] 3 1 3 0 1 2 2 1 3 1 4 3 0 1 0 0 1 0 0 2 3 3 3 0 0 1 1 0 1 2 3 0 0 2 1 1
## [5653] 1 0 2 0 0 4 2 3 3 0 0 0 0 1 0 0 1 4 1 1 2 1 3 3 0 3 0 1 1 0 2 2 0 0 0 0
## [5689] 4 1 2 0 1 2 0 1 0 1 2 1 0 1 1 2 1 0 2 1 2 2 0 2 3 2 0 2 1 0 0 0 2 2 2 2
## [5725] 2 3 2 3 0 0 1 2 1 1 1 0 3 1 0 3 0 2 0 2 3 0 0 2 1 0 4 0 0 3 1 3 2 2 0 3
## [5761] 1 2 2 2 2 1 1 3 0 2 2 0 3 1 2 1 2 2 1 3 1 0 1 0 0 1 0 2 0 1 2 1 0 1 1 2
## [5797] 2 2 1 3 3 1 1 2 2 2 2 4 2 2 0 1 2 3 0 3 1 2 0 0 0 2 0 2 2 2 3 0 1 3 2 0
## [5833] 0 2 0 0 2 2 2 1 3 2 2 1 0 0 3 0 1 2 1 1 2 1 1 2 1 0 0 0 3 1 3 0 0 2 3 1
## [5869] 3 0 1 1 1 0 0 3 2 2 2 0 1 0 1 1 0 1 3 2 2 1 3 0 0 4 2 1 0 4 2 1 4 1 0 2
## [5905] 2 3 3 2 1 3 0 0 0 0 0 0 0 4 2 0 0 0 2 1 4 0 3 0 0 2 1 2 0 1 1 1 0 2 4 1
## [5941] 1 0 0 1 1 2 0 2 1 2 1 3 1 3 1 1 1 2 0 2 2 0 2 0 3 2 0 3 0 1 1 4 0 1 1 3
## [5977] 2 3 1 0 2 0 1 2 3 3 3 2 1 1 2 0 0 0 0 0 0 1 2 1 2 3 2 2 1 1 2 1 0 0 1 2
## [6013] 1 1 2 3 1 0 1 1 0 1 1 2 2 0 0 0 2 0 0 3 1 3 2 0 3 1 0 0 3 0 2 2 0 1 1 2
## [6049] 0 1 2 3 3 2 3 1 2 2 0 0 2 0 0 0 2 1 3 0 0 2 0 2 2 1 0 1 0 3 3 2 2 2 2 2
## [6085] 1 0 1 1 0 3 2 1 2 0 2 3 0 2 2 2 3 3 1 1 0 3 1 0 3 3 1 0 0 1 3 1 1 0 3 0
## [6121] 3 2 0 0 1 3 0 1 2 1 0 2 0 2 3 4 0 1 2 4 2 2 0 0 3 2 2 1 2 2 1 3 0 3 3 1
## [6157] 0 1 3 2 3 2 0 2 0 0 2 0 1 0 1 2 1 0 2 2 2 2 3 3 0 1 0 2 3 0 3 1 0 3 1 0
## [6193] 3 3 2 0 3 0 2 3 1 2 0 0 3 1 2 3 0 0 2 3 1 2 1 3 2 3 1 2 1 1 2 1 0 1 0 1
## [6229] 0 2 2 3 3 0 3 1 2 1 1 3 1 1 4 1 3 4 2 0 0 4 1 2 0 1 2 1 2 1 1 0 1 2 1 2
## [6265] 0 2 3 1 0 3 0 0 0 2 0 2 2 0 0 3 1 0 2 1 2 3 3 3 1 4 2 2 1 0 3 3 1 3 4 3
## [6301] 0 2 0 2 2 0 2 1 1 2 2 1 1 3 0 0 3 1 0 0 1 1 2 2 1 3 3 2 3 1 2 0 1 0 0 2
## [6337] 0 1 3 2 2 2 0 1 1 0 2 2 0 3 2 3 0 1 1 1 2 2 1 1 0 2 2 2 2 2 3 2 0 2 1 4
## [6373] 2 1 1 3 2 0 1 2 3 0 3 1 0 0 1 2 1 1 0 1 0 2 2 2 2 2 3 1 0 1 2 4 3 0 2 2
## [6409] 4 0 2 0 0 0 0 1 2 3 0 3 1 2 1 2 1 2 3 0 4 4 2 2 3 0 3 0 0 0 2 1 3 2 0 3
## [6445] 2 3 2 1 1 0 0 0 3 3 3 4 2 0 0 0 2 3 3 2 1 4 2 2 2 0 4 3 2 1 4 1 2 2 2 1
## [6481] 0 2 2 2 0 1 2 2 3 1 0 0 1 2 1 0 1 0 4 2 1 0 0 2 0 1 1 3 1 1 3 0 3 2 2 1
## [6517] 0 3 2 0 3 0 0 3 2 0 0 1 0 1 0 0 0 0 0 3 1 2 0 2 2 4 0 0 3 1 3 0 2 2 2 1
## [6553] 4 2 2 1 0 1 2 0 0 3 2 1 0 1 1 1 2 2 1 3 2 1 3 1 2 3 3 3 2 0 1 2 2 2 0 3
## [6589] 3 3 0 3 1 0 0 2 0 0 3 2 3 0 2 0 3 1 0 0 3 0 1 1 0 2 3 0 2 1 0 3 2 2 0 2
## [6625] 3 1 0 0 1 3 3 1 3 0 2 2 2 4 3 2 2 0 0 1 1 1 3 0 3 1 0 3 2 3 0 0 0 3 2 1
## [6661] 0 4 1 2 1 1 1 4 1 2 2 1 2 0 2 1 0 1 3 2 3 1 2 2 1 3 1 1 0 4 2 2 0 0 0 2
## [6697] 1 3 3 0 2 0 1 2 0 2 1 0 2 2 2 0 3 3 2 0 0 4 3 2 0 1 3 2 2 2 2 1 0 4 2 0
## [6733] 0 1 4 1 0 4 2 4 1 1 3 4 1 1 1 3 1 1 1 4 0 1 0 0 2 0 1 3 0 2 3 0 0 0 2 4
## [6769] 2 3 3 4 0 2 0 1 0 0 1 2 1 3 1 0 4 3 3 0 2 3 0 1 0 0 2 2 4 1 1 0 1 1 2 2
## [6805] 0 3 2 0 0 4 2 2 2 0 0 1 3 0 3 3 3 1 2 1 0 4 0 3 2 1 1 0 0 1 4 2 2 2 1 0
## [6841] 0 0 3 0 2 0 4 2 0 2 0 0 0 3 2 1 2 1 3 1 0 2 1 1 1 4 0 2 0 2 2 2 2 1 0 2
## [6877] 0 2 2 0 0 1 0 2 2 0 0 1 4 3 2 3 2 0 2 0 2 3 2 1 1 0 0 2 2 2 0 3 3 1 2 0
## [6913] 3 1 0 3 1 3 1 0 1 1 1 0 1 0 2 4 3 2 0 1 3 3 0 0 3 1 0 0 0 4 2 0 0 1 3 0
## [6949] 2 1 0 0 1 4 0 3 3 2 2 1 2 2 3 2 0 1 0 0 3 0 1 4 0 1 2 1 1 1 1 3 3 2 0 0
## [6985] 2 0 4 0 3 2 3 0 3 3 0 2 1 0 0 4 1 3 0 1 2 2 3 0 1 3 2 0 2 3 0 1 2 4 0 0
## [7021] 2 0 0 2 0 1 1 2 2 2 2 3 2 0 1 0 0 0 0 2 2 3 2 2 3 2 1 0 1 0 0 1 0 0 0 1
## [7057] 1 0 2 0 4 1 1 0 2 2 0 2 3 2 2 0 0 1 0 2 0 2 3 0 1 3 0 2 0 1 1 1 0 4 0 0
## [7093] 1 0 2 4 2 0 1 1 3 2 1 0 0 0 0 0 1 3 0 3 1 0 0 0 2 3 3 3 1 1 0 1 3 1 3 0
## [7129] 2 3 0 0 0 2 1 4 1 2 0 1 0 0 0 2 0 0 2 3 3 1 3 0 0 1 0 3 1 2 0 3 0 3 0 0
## [7165] 1 4 2 0 0 0 2 1 3 0 3 3 2 1 0 2 3 1 0 0 1 1 0 2 1 2 2 2 1 2 0 2 2 0 2 0
## [7201] 1 1 2 3 0 1 1 3 0 3 1 2 1 1 1 3 2 3 1 0 3 2 3 1 2 0 2 3 2 1 0 2 3 1 0 2
## [7237] 3 1 1 3 1 4 3 2 1 1 0 2 3 2 2 2 0 3 0 0 0 3 2 1 4 2 1 1 0 3 0 0 0 0 3 2
## [7273] 2 0 0 3 1 2 2 0 2 3 0 0 2 0 3 3 0 1 2 0 3 2 3 2 2 2 3 0 2 3 0 2 0 0 1 0
## [7309] 1 3 0 3 0 1 1 0 2 0 0 0 1 1 1 0 2 0 2 2 1 2 2 0 3 3 2 0 4 0 4 3 2 1 3 2
## [7345] 2 0 1 2 0 1 2 3 1 0 2 3 3 2 2 2 1 0 2 2 1 0 1 1 1 2 2 2 1 2 3 2 1 1 2 1
## [7381] 2 3 0 0 3 2 1 0 3 3 3 2 3 0 1 0 0 0 0 1 2 1 1 1 0 3 1 3 1 3 1 2 1 3 0 2
## [7417] 1 0 4 3 2 1 1 1 2 1 1 0 2 4 3 2 0 0 2 2 2 0 0 2 0 2 3 0 0 2 2 2 0 2 3 1
## [7453] 1 0 1 2 2 0 0 0 1 2 1 0 4 1 0 2 0 2 0 2 1 1 0 2 0 2 1 2 2 0 0 2 3 1 0 4
## [7489] 1 1 4 0 2 2 2 1 2 2 2 1 4 0 0 2 1 3 0 1 0 0 2 0 2 0 3 4 4 0 0 2 2 0 1 0
## [7525] 1 0 0 2 2 2 3 2 3 1 0 2 3 1 4 2 0 0 1 0 1 3 3 0 1 0 0 2 4 2 2 1 1 0 0 3
## [7561] 0 0 2 2 3 1 2 3 3 2 2 1 0 2 0 2 0 4 3 0 2 0 0 0 0 0 1 3 3 1 2 0 0 1 0 1
## [7597] 2 4 0 0 1 0 0 1 1 0 0 3 0 2 3 2 4 1 0 2 1 0 3 2 3 3 1 3 4 0 2 2 0 3 2 0
## [7633] 4 0 3 2 2 1 0 2 3 1 2 3 1 1 1 1 2 3 0 1 0 3 0 1 2 0 1 0 2 1 2 3 0 1 0 4
## [7669] 2 1 1 2 2 1 1 1 1 2 1 0 3 2 2 0 0 2 0 0 3 3 2 0 0 0 2 1 0 2 2 1 1 0 0 2
## [7705] 0 1 3 1 3 3 0 2 0 1 4 1 0 0 0 2 3 0 0 2 0 4 3 2 0 1 0 0 0 0 0 0 0 0 2 0
## [7741] 0 2 0 2 2 2 2 1 1 0 1 2 2 0 2 1 0 0 1 2 3 3 3 1 1 4 0 0 0 1 2 2 2 0 1 4
## [7777] 1 4 2 2 3 0 2 2 3 2 2 0 3 1 0 2 1 1 1 2 3 2 1 3 3 1 2 4 0 2 4 1 1 0 3 0
## [7813] 2 1 0 2 3 0 2 2 3 0 1 2 0 3 4 0 2 3 1 1 0 2 0 0 1 3 3 2 2 3 0 0 0 0 2 0
## [7849] 3 1 2 0 2 2 2 2 1 1 0 1 2 2 2 3 2 1 3 3 1 3 2 0 1 2 0 0 0 2 0 3 0 3 2 2
## [7885] 1 1 2 2 0 0 0 0 2 1 0 1 1 4 2 1 0 0 2 3 1 1 1 2 2 2 0 2 1 2 1 4 0 2 0 1
## [7921] 2 2 2 0 1 1 1 2 1 0 0 0 1 1 3 1 2 1 1 0 3 3 1 1 3 3 1 3 3 1 2 1 0 1 2 0
## [7957] 2 2 1 0 2 3 3 1 2 2 2 1 0 2 1 2 4 0 1 2 2 2 0 3 0 3 0 1 3 0 2 3 1 2 3 1
## [7993] 2 4 0 1 0 1 2 2 2 2 1 0 1 1 2 4 0 2 1 1 2 0 2 0 0 0 3 0 2 1 1 0 1 2 3 2
## [8029] 3 0 1 2 1 2 4 3 3 0 1 0 0 3 0 3 0 3 1 1 0 3 0 2 1 2 0 0 3 0 2 2 2 2 1 4
## [8065] 3 0 2 2 0 0 1 3 0 0 0 2 0 3 2 1 1 0 0 2 1 2 0 1 2 0 2 1 0 1 2 0 1 0 3 2
## [8101] 1 2 2 2 0 2 1 2 2 1 2 0 1 2 0 0 3 0 2 0 1 2 3 2 0 2 2 1 0 4 0 0 2 1 1 0
## [8137] 1 3 2 4 2 0 3 0 0 1 2 0 2 2 0 1 2 3 2 3 1 1 0 1 1 2 2 3 1 2 0 3 0 2 3 0
## [8173] 1 2 0 3 3 2 2 0 3 1 3 0 0 2 2 1 2 3 3 0 2 3 0 2 0 3 3 3 1 4 1 2 1 2 2 3
## [8209] 2 3 1 1 1 2 0 3 0 1 0 4 2 4 1 1 1 0 1 3 2 2 2 2 2 2 0 3 3 0 3 1 0 0 0 2
## [8245] 3 0 1 1 1 2 4 3 0 0 2 2 0 0 4 1 4 2 3 1 1 1 1 1 1 3 2 1 0 1 0 0 0 2 2 1
## [8281] 4 2 2 0 2 1 0 2 3 0 2 0 0 0 2 0 3 2 0 2 3 0 3 0 2 2 3 0 3 0 2 2 2 2 2 1
## [8317] 1 3 2 3 1 2 0 2 1 1 3 1 1 0 2 2 0 2 3 0 0 3 2 2 2 0 2 2 2 2 0 0 2 3 0 2
## [8353] 2 0 1 2 0 3 3 3 1 0 1 2 0 3 2 4 0 2 0 0 4 2 0 1 2 1 1 0 0 2 0 3 1 0 2 1
## [8389] 2 1 1 0 2 2 0 4 1 2 1 0 1 2 3 1 0 2 3 4 0 0 2 0 0 0 0 2 0 0 3 1 2 2 1 1
## [8425] 3 0 2 2 1 3 0 1 4 1 3 2 2 0 2 1 2 0 0 1 3 1 0 0 3 0 2 0 1 3 0 3 0 2 1 0
## [8461] 2 0 2 0 1 3 3 4 1 1 0 3 0 0 2 3 1 1 2 3 2 1 0 1 3 2 1 2 1 2 0 1 3 3 3 2
## [8497] 0 1 0 1 1 1 2 0 0 0 0 1 2 3 1 0 3 3 2 1 2 2 3 2 0 3 1 0 4 2 2 0 2 3 3 3
## [8533] 2 3 0 0 0 4 3 2 0 3 3 0 3 2 2 3 0 2 0 1 4 0 3 0 2 1 0 2 3 2 0 3 0 1 0 0
## [8569] 0 4 0 4 3 0 1 0 0 2 4 1 0 3 2 0 0 3 0 3 2 0 3 0 0 3 4 2 0 2 0 1 0 2 0 2
## [8605] 0 4 0 3 0 0 1 1 0 2 2 2 2 2 0 2 1 1 0 2 0 1 0 1 0 3 3 1 1 2 3 0 0 0 2 0
## [8641] 0 1 0 0 1 3 3 1 2 1 0 2 2 3 0 2 1 0 0 2 2 2 0 0 0 2 0 2 2 1 3 2 2 0 1 2
## [8677] 2 2 1 2 2 2 0 2 2 1 2 0 3 2 1 1 1 2 2 1 1 0 0 0 0 1 1 3 3 2 2 2 0 2 0 1
## [8713] 2 1 3 1 0 3 2 1 0 1 1 2 3 0 0 3 1 0 0 0 1 1 0 2 2 0 3 1 2 2 0 2 0 0 4 0
## [8749] 0 1 0 3 3 0 2 3 1 0 2 2 0 2 0 4 1 0 0 3 4 3 3 2 1 0 1 1 4 0 0 1 3 3 3 2
## [8785] 0 3 4 0 0 0 3 2 3 1 0 3 0 0 3 0 2 2 3 2 0 0 1 1 4 1 3 0 2 0 3 2 2 1 2 3
## [8821] 3 0 2 1 4 2 1 2 0 0 2 2 2 3 4 1 0 1 1 0 2 3 1 1 3 0 0 1 2 2 3 2 2 3 2 2
## [8857] 2 0 1 0 1 3 4 3 0 2 0 0 0 1 3 0 0 2 2 0 0 0 0 1 3 1 2 0 2 2 3 2 4 0 0 4
## [8893] 0 3 1 3 2 1 0 0 1 4 3 3 0 4 0 0 3 1 2 2 1 4 2 1 1 1 1 2 1 1 2 0 2 2 0 0
## [8929] 1 0 0 2 0 0 1 0 0 3 0 3 2 1 3 0 2 1 1 1 1 0 2 0 1 0 3 2 1 4 1 1 0 3 3 2
## [8965] 1 1 0 3 0 0 3 1 2 2 3 1 2 4 3 2 1 1 2 2 2 2 2 2 2 4 2 2 1 2 1 3 0 0 1 2
## [9001] 3 0 1 1 1 2 3 2 2 3 0 2 0 1 2 2 1 0 1 3 3 0 3 0 2 0 1 0 1 1 0 0 2 1 0 1
## [9037] 3 1 0 3 1 2 3 3 3 0 0 1 1 0 0 1 1 3 0 0 0 0 4 2 4 1 2 1 1 2 2 3 4 2 1 2
## [9073] 2 1 4 2 3 4 0 3 0 0 2 0 1 3 0 2 0 4 1 0 0 2 3 0 3 3 1 3 0 2 0 0 2 2 1 0
## [9109] 3 2 1 2 1 2 1 2 1 1 2 3 0 0 1 3 3 1 3 0 0 0 2 3 2 3 0 1 3 3 0 0 0 1 1 3
## [9145] 0 3 3 0 2 1 3 0 3 0 1 2 2 0 2 2 0 2 0 0 2 2 2 4 2 1 1 0 0 0 0 2 0 1 2 2
## [9181] 3 1 0 1 2 2 1 1 2 3 1 3 1 0 1 0 3 0 3 2 3 3 1 2 0 3 1 3 1 3 1 0 1 0 0 1
## [9217] 0 2 3 3 0 1 2 3 1 1 3 2 3 1 1 2 3 4 3 2 0 3 0 2 0 1 0 3 2 0 1 0 0 3 3 2
## [9253] 1 2 2 2 0 2 2 1 1 2 2 1 2 0 3 3 3 2 0 2 0 0 2 1 0 3 0 1 1 3 2 0 0 2 2 1
## [9289] 3 4 3 0 3 0 2 0 3 0 2 2 1 2 0 4 3 3 2 1 1 2 0 0 1 2 0 1 2 2 3 1 0 0 3 2
## [9325] 0 1 4 1 3 2 0 1 0 2 2 4 1 2 1 1 1 2 3 2 1 1 3 0 1 1 1 0 1 0 3 1 0 3 1 1
## [9361] 2 2 0 1 1 1 0 4 0 0 2 2 2 2 3 4 2 2 2 0 0 0 2 0 2 3 0 3 2 0 1 0 0 1 0 0
## [9397] 2 0 2 2 2 0 1 0 0 2 3 2 3 1 2 3 3 3 4 3 1 1 2 1 2 2 2 1 2 1 3 1 0 0 1 0
## [9433] 2 3 0 3 1 0 2 2 2 0 3 3 2 0 3 2 1 2 0 1 2 1 1 2 2 1 1 1 2 3 0 4 4 2 3 2
## [9469] 2 2 3 2 4 0 3 0 0 2 1 2 0 0 3 0 1 3 0 3 3 0 0 4 1 0 3 0 3 1 4 0 0 1 1 1
## [9505] 1 3 2 1 0 1 0 0 1 2 0 0 2 1 1 2 0 3 3 1 0 0 2 2 1 1 0 0 0 1 0 2 2 1 3 2
## [9541] 0 1 0 2 3 3 3 2 1 0 1 0 0 3 0 3 2 1 2 0 4 3 3 0 1 2 1 0 2 2 0 0 1 0 0 0
## [9577] 1 0 0 1 0 1 2 2 2 1 3 3 0 0 0 2 1 2 0 1 3 0 0 0 1 0 3 3 2 0 3 0 0 0 3 2
## [9613] 0 1 2 3 1 1 2 2 0 1 0 3 1 2 0 3 3 2 2 4 2 0 1 0 3 2 0 1 0 0 0 1 0 2 4 1
## [9649] 0 0 2 1 0 1 0 3 0 4 2 2 1 0 1 2 3 2 0 2 1 0 2 1 2 2 0 0 1 2 0 2 4 0 1 4
## [9685] 0 3 4 1 0 0 2 3 0 0 1 0 0 1 3 0 2 2 3 3 2 2 1 2 0 0 1 3 2 3 1 1 1 2 0 2
## [9721] 0 3 0 1 1 0 0 1 3 2 2 1 2 0 0 0 0 0 2 2 2 2 4 0 2 2 3 2 0 1 3 0 1 0 0 2
## [9757] 0 0 1 3 2 1 1 2 3 1 0 0 4 3 2 3 0 3 4 1 0 3 0 0 2 0 2 0 2 0 2 2 2 3 0 4
## [9793] 0 0 2 1 3 3 1 0 2 1 1 3 4 1 2 1 0 1 3 1 1 0 0 0 0 1 0 2 2 0 0 0 0 0 2 1
## [9829] 0 2 1 1 0 0 3 0 0 1 1 0 0 2 1 0 1 3 0 1 0 2 1 0 3 2 0 2 3 1 1 2 4 1 2 3
## [9865] 2 0 2 1 3 3 2 2 0 1 4 1 0 1 4 0 2 2 2 1 2 3 0 4 2 3 2 0 0 0 0 0 0 2 3 0
## [9901] 0 1 0 1 1 0 1 3 2 4 4 2 3 0 4 0 3 2 0 1 1 2 1 1 0 2 2 0 2 0 4 2 4 0 2 0
## [9937] 0 2 3 3 2 0 1 0 1 3 3 2 1 0 2 2 2 3 2 0 2 4 0 0 1 3 2 0 0 2 2 2 3 2 1 1
## [9973] 2 0 2 1 1 3 0 4 1 1 0 1 1 0 1 2 1 0 2 1 2 3 1 1 1 3 3 0 2 0 3 3 3 4 1 0
## [10009] 4 1 4 1 0 1 2 4 2 0 3 3 3 2 0 0 1 2 0 0 3 0 0 2 0 3 2 0 1 2 2 2 2 0 2 2
## [10045] 2 2 1 0 2 2 2 2 2 1 0 0 0 0 1 0 1 3 0 3 2 1 1 0 1 2 2 0 3 3 2 0 0 2 0 2
## [10081] 3 3 3 3 2 0 0 4 1 0 1 3 0 1 3 0 0 4 3 0 2 2 0 0 0 2 3 1 0 2 3 2 2 1 1 0
## [10117] 1 3 0 2 1 0 0 3 0 1 2 2 0 0 3 1 2 2 0 0 1 2 0 0 1 4 3 2 2 0 2 1 0 1 1 0
## [10153] 0 1 0 0 3 3 4 1 3 0 2 0 0 2 4 0 2 4 2 3 1 0 2 2 3 4 2 2 3 4 2 0 3 0 0 1
## [10189] 2 2 3 3 2 3 3 0 0 0 3 0 2 2 1 3 0 2 3 2 1 3 0 2 0 0 0 2 0 0 2 0 2 2 1 0
## [10225] 1 0 0 0 3 4 1 1 0 1 2 3 0 1 3 2 4 2 1 1 1 2 3 2 1 2 4 3 2 3 0 3 0 1 1 2
## [10261] 4 2 2 0 3 2 2 1 2 3 1 1 2 2 1 0 2 3 3 2 3 1 1 1 2 1 2 0 2 0 3 3 1 0 3 3
## [10297] 0 3 2 3 1 1 0 0 2 0 2 3 0 2 0 3 4 3 0 1 1 0 3 0 2 2 0 4 1 4 0 0 0 0 0 2
## [10333] 1 0 1 2 1 2 3 2 1 0 0 3 1 0 0 0 0 0 0 0 2 0 1 2 0 0 2 0 1 2 4 1 2 1 3 0
## [10369] 3 3 2 0 1 1 2 3 1 2 0 3 2 2 0 3 0 1 0 0 2 4 2 0 0 0 2 2 1 1 0 0 2 2 2 0
## [10405] 0 4 0 0 1 2 3 2 2 2 1 2 1 2 1 3 2 0 0 2 3 3 0 2 0 2 3 2 3 0 0 2 3 2 3 0
## [10441] 2 3 1 2 0 2 2 2 2 1 0 0 1 2 3 0 1 1 0 2 2 3 3 1 2 1 0 1 4 0 1 0 0 0 1 0
## [10477] 0 1 1 2 2 2 3 3 0 3 1 0 4 2 0 1 3 2 2 2 0 0 2 3 0 1 2 2 1 2 2 0 1 0 1 1
## [10513] 1 0 2 0 2 3 2 0 0 1 3 1 1 3 2 2 2 0 0 1 1 1 1 0 2 2 0 2 0 0 0 1 0 3 2 0
## [10549] 0 2 4 1 1 2 2 1 4 1 1 0 0 1 0 0 4 0 3 2 2 2 0 3 2 1 3 1 2 0 1 2 2 2 1 1
## [10585] 4 2 0 3 0 2 2 0 3 3 2 1 0 1 0 1 4 0 3 1 0 1 1 0 3 3 3 0 2 0 1 2 1 4 1 1
## [10621] 1 0 2 3 1 1 1 2 2 2 1 3 2 1 2 1 2 1 2 0 2 0 1 1 1 3 0 1 2 3 1 2 1 3 0 1
## [10657] 3 0 3 3 0 4 0 2 3 0 3 0 4 0 0 0 1 0 3 1 3 4 0 0 0 3 0 1 2 1 1 0 1 2 3 2
## [10693] 1 0 1 2 1 3 1 1 3 2 1 1 2 0 1 2 0 1 1 2 0 3 2 0 0 0 0 1 1 1 1 1 2 1 0 0
## [10729] 2 0 0 3 3 0 0 0 0 0 1 0 2 0 4 0 0 0 0 1 0 4 1 1 1 0 1 2 1 0 2 2 3 0 0 2
## [10765] 3 2 1 0 4 1 3 0 1 1 3 4 2 1 0 0 1 1 2 3 1 2 3 2 1 2 2 2 0 3 2 1 4 3 1 0
## [10801] 1 0 2 3 3 3 2 0 2 0 0 3 2 1 0 0 0 0 2 1 2 0 1 0 2 3 0 3 4 2 0 0 0 2 0 0
## [10837] 1 3 2 2 2 0 4 4 0 0 0 2 2 1 2 0 0 3 1 0 1 0 1 1 2 1 1 2 3 2 3 2 2 0 0 1
## [10873] 1 3 2 2 0 0 3 0 1 4 3 0 0 1 0 0 1 3 0 3 1 2 2 0 1 0 0 0 1 2 1 0 1 4 0 0
## [10909] 1 2 1 0 0 2 2 0 1 4 2 2 2 1 0 1 1 3 1 2 2 3 0 4 0 2 3 1 0 0 0 0 1 2 2 3
## [10945] 2 0 3 2 2 2 1 2 1 2 4 3 2 2 1 1 0 2 2 1 0 0 1 2 1 1 3 2 1 1 1 3 2 0 0 0
## [10981] 2 2 1 2 1 1 2 0 3 1 3 3 4 0 3 3 0 2 0 1 3 0 3 2 3 2 0 2 3 3 3 0 1 3 0 0
## [11017] 2 1 3 1 0 1 0 0 0 2 3 3 3 1 0 2 2 4 2 0 1 0 0 0 1 3 0 2 3 0 2 3 0 3 3 0
## [11053] 2 2 2 3 1 1 1 3 4 1 0 0 2 2 2 1 1 2 0 0 2 0 1 2 2 1 2 0 4 2 0 3 0 3 0 3
## [11089] 0 1 4 4 0 1 4 2 3 1 3 2 0 2 0 2 3 2 2 1 0 3 1 0 0 0 1 1 0 0 0 2 0 2 0 1
## [11125] 0 2 0 1 3 0 2 1 2 1 2 3 0 0 0 2 0 2 1 3 1 0 1 0 0 1 1 1 3 2 0 2 0 1 3 2
## [11161] 0 0 1 2 2 1 0 2 3 2 1 1 0 0 1 2 2 0 1 1 1 2 2 2 1 0 2 1 0 2 2 1 3 3 4 2
## [11197] 0 0 0 4 1 2 2 2 1 1 2 0 2 3 2 2 4 2 0 2 1 2 2 0 3 1 0 4 2 3 0 1 0 0 0 1
## [11233] 2 2 3 1 2 1 2 2 2 2 2 2 0 3 0 1 0 3 1 0 1 0 3 1 0 2 1 3 1 2 2 1 2 2 0 1
## [11269] 3 0 3 1 2 3 1 2 1 1 4 2 1 1 1 3 2 0 3 1 0 0 2 1 1 3 4 0 1 2 0 1 1 0 2 2
## [11305] 3 2 2 0 3 0 1 1 1 1 4 3 1 0 0 1 0 0 2 3 0 3 3 2 1 2 3 0 1 3 0 3 0 3 0 0
## [11341] 2 0 0 0 1 0 0 3 0 3 0 2 0 2 2 2 2 0 0 0 0 3 2 1 1 1 0 4 0 2 1 2 3 0 3 2
## [11377] 0 0 2 1 0 0 1 2 2 1 0 0 3 0 2 1 1 0 2 1 2 2 3 2 4 1 2 2 3 0 3 4 0 4 2 0
## [11413] 0 0 0 2 0 1 0 0 0 0 1 0 0 3 2 3 0 0 2 0 0 2 3 1 0 2 0 1 2 3 0 2 0 3 2 2
## [11449] 2 1 1 3 0 0 3 2 1 2 0 0 1 2 0 3 1 1 3 1 3 0 0 2 0 2 2 1 0 0 2 4 0 2 2 2
## [11485] 2 3 2 0 1 0 0 0 2 2 2 1 2 3 3 1 1 0 0 4 1 0 4 0 0 0 0 0 0 3 2 2 0 1 3 3
## [11521] 2 2 0 0 0 2 2 0 2 3 2 1 2 2 0 2 1 0 0 3 0 0 0 1 0 2 1 2 1 1 2 0 2 1 2 2
## [11557] 1 1 1 2 2 0 2 0 2 2 0 1 2 2 1 2 1 2 0 2 2 1 0 0 0 0 2 1 3 0 3 2 0 0 3 1
## [11593] 2 4 2 1 0 1 1 0 1 2 1 0 3 0 4 2 0 2 0 0 0 3 1 2 1 2 3 0 0 3 4 3 0 1 0 1
## [11629] 4 1 0 2 2 2 2 0 3 2 0 0 1 0 2 1 1 3 0 3 3 2 3 0 1 3 4 3 2 0 3 2 1 0 2 3
## [11665] 0 1 0 0 2 0 0 4 0 3 1 2 2 1 4 1 3 0 4 2 2 0 3 3 1 3 0 2 3 1 0 2 0 0 0 2
## [11701] 0 1 2 2 1 1 3 3 2 0 2 3 0 3 0 0 3 0 3 0 3 0 1 3 2 1 0 0 0 4 0 3 2 4 3 2
## [11737] 2 2 3 4 2 3 2 2 1 0 0 4 0 0 2 1 0 0 0 2 0 2 2 2 1 1 2 2 1 2 2 1 2 0 3 1
## [11773] 0 2 1 2 0 1 1 3 3 3 1 1 3 1 3 0 0 0 0 0 2 3 0 2 1 3 0 2 2 2 0 1 2 1 1 2
## [11809] 0 2 0 3 2 2 0 3 1 4 0 0 0 2 2 3 3 2 0 2 3 2 1 0 1 2 3 2 0 4 0 1 0 2 0 2
## [11845] 0 3 0 2 3 1 0 1 0 2 3 0 2 2 0 0 1 3 2 0 3 2 0 2 3 4 4 0 4 2 0 2 1 2 0 2
## [11881] 3 2 3 0 2 1 0 1 2 0 0 3 2 0 3 0 0 1 0 2 0 2 0 1 0 3 3 1 3 2 3 0 0 0 2 0
## [11917] 0 0 2 2 3 0 2 2 4 1 0 2 1 3 0 0 0 2 2 0 0 4 1 2 2 2 2 4 2 4 1 2 1 1 2 2
## [11953] 0 2 2 2 2 1 0 1 3 4 3 3 0 0 0 1 1 0 2 2 0 2 1 1 2 0 2 1 2 2 2 0 1 0 0 3
## [11989] 0 1 0 3 2 3 0 1 1 4 0 0 0 3 0 2 1 0 3 1 0 0 3 2 3 0 3 2 3 0 1 2 2 0 3 0
## [12025] 2 3 0 2 0 1 3 0 3 0 2 3 0 2 2 2 2 0 0 0 0 0 2 3 0 3 1 3 2 1 3 3 0 2 1 1
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## [12529] 1 0 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 1 1 0 0 0 1 1 1 0 1 1 0 1 0 1 1 1
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## [12601] 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1
## [12637] 1 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0 1 0 1 1 1
## [12673] 0 0 1 1 1Explanation: I replacces th NA values in Purchased and STARS with zeros in order to keep enough data entries and have a value for the ones that did not.
summary(mydata$TotalSulfurDioxide)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.0 100.0 154.0 204.3 262.0 1057.0 1290plot(mydata$TotalSulfurDioxide)
hist(mydata$TotalSulfurDioxide)
summary(mydata$TotalSulfurDioxide)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.0 100.0 154.0 204.3 262.0 1057.0 1290plot(mydata$TotalSulfurDioxide)
hist(mydata$TotalSulfurDioxide)
mydata=mydata
mydata <- subset (mydata, select = -INDEX)TASK 2: MODELING
I will be conducting my model on the Purchase variable, which would make my models be logistic models since the response variable is binomial.
My first model is just a test:
model1=glm(mydata$Purchase~mydata$FixedAcidity+mydata$VolatileAcidity+mydata$CitricAcid, family='binomial')
model1##
## Call: glm(formula = mydata$Purchase ~ mydata$FixedAcidity + mydata$VolatileAcidity +
## mydata$CitricAcid, family = "binomial")
##
## Coefficients:
## (Intercept) mydata$FixedAcidity mydata$VolatileAcidity
## 1.65051 -0.02499 -0.25791
## mydata$CitricAcid
## 0.04063
##
## Degrees of Freedom: 12023 Total (i.e. Null); 12020 Residual
## (653 observations deleted due to missingness)
## Null Deviance: 12480
## Residual Deviance: 12400 AIC: 12410summary(model1)##
## Call:
## glm(formula = mydata$Purchase ~ mydata$FixedAcidity + mydata$VolatileAcidity +
## mydata$CitricAcid, family = "binomial")
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -1.9381 0.6136 0.6578 0.7089 1.0753
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.650511 0.056005 29.471 < 2e-16 ***
## mydata$FixedAcidity -0.024993 0.004317 -5.790 7.04e-09 ***
## mydata$VolatileAcidity -0.257911 0.038028 -6.782 1.18e-11 ***
## mydata$CitricAcid 0.040628 0.037344 1.088 0.277
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 12483 on 12023 degrees of freedom
## Residual deviance: 12404 on 12020 degrees of freedom
## (653 observations deleted due to missingness)
## AIC: 12412
##
## Number of Fisher Scoring iterations: 4My second model runs on all of the response variables. However, this includes the Cases variable, which should be ommitted because if there are cases, it has obviously been purchased. Although this is the best model, as seen with the lowest AIC value, it doesn’t do us quite that much in terms of telling us whether or not the wine has been purchased. We need to focus on the other variables.
model2=glm(Purchase~.,data=mydata, family='binomial')## Warning: glm.fit: algorithm did not converge## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurredmodel2##
## Call: glm(formula = Purchase ~ ., family = "binomial", data = mydata)
##
## Coefficients:
## (Intercept) Cases STARS FixedAcidity
## -2.297e+01 4.294e+01 -1.641e-01 -3.086e-03
## VolatileAcidity CitricAcid ResidualSugar Chlorides
## 2.286e-01 -1.140e-02 -3.120e-03 2.112e-01
## FreeSulfurDioxide TotalSulfurDioxide Density pH
## -4.974e-04 5.135e-04 -1.451e-01 -1.390e-01
## Sulphates Alcohol LabelAppeal AcidIndex
## -4.421e-02 -3.789e-02 1.107e+00 -7.931e-03
##
## Degrees of Freedom: 8596 Total (i.e. Null); 8581 Residual
## (4080 observations deleted due to missingness)
## Null Deviance: 8860
## Residual Deviance: 8.656e-07 AIC: 32summary(model2)##
## Call:
## glm(formula = Purchase ~ ., family = "binomial", data = mydata)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.734e-05 2.100e-08 2.100e-08 2.100e-08 1.192e-04
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -2.297e+01 3.678e+04 -0.001 1.000
## Cases 4.294e+01 1.998e+03 0.021 0.983
## STARS -1.641e-01 1.603e+03 0.000 1.000
## FixedAcidity -3.086e-03 1.985e+02 0.000 1.000
## VolatileAcidity 2.286e-01 1.524e+03 0.000 1.000
## CitricAcid -1.140e-02 1.489e+03 0.000 1.000
## ResidualSugar -3.120e-03 3.690e+01 0.000 1.000
## Chlorides 2.112e-01 3.875e+03 0.000 1.000
## FreeSulfurDioxide -4.974e-04 8.164e+00 0.000 1.000
## TotalSulfurDioxide 5.135e-04 5.798e+00 0.000 1.000
## Density -1.451e-01 3.636e+04 0.000 1.000
## pH -1.390e-01 1.457e+03 0.000 1.000
## Sulphates -4.421e-02 1.401e+03 0.000 1.000
## Alcohol -3.789e-02 2.683e+02 0.000 1.000
## LabelAppeal 1.107e+00 1.391e+03 0.001 0.999
## AcidIndex -7.931e-03 6.218e+02 0.000 1.000
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 8.8598e+03 on 8596 degrees of freedom
## Residual deviance: 8.6560e-07 on 8581 degrees of freedom
## (4080 observations deleted due to missingness)
## AIC: 32
##
## Number of Fisher Scoring iterations: 25This model 4 is run without Cases and STARS. It has significantly improves from my first test model, as seen by the AIC.
model4=glm(Purchase~FixedAcidity+VolatileAcidity+CitricAcid+ResidualSugar+Chlorides+FreeSulfurDioxide+Density+pH+Sulphates+Alcohol+LabelAppeal+AcidIndex,data=mydata,family="binomial")
model4##
## Call: glm(formula = Purchase ~ FixedAcidity + VolatileAcidity + CitricAcid +
## ResidualSugar + Chlorides + FreeSulfurDioxide + Density +
## pH + Sulphates + Alcohol + LabelAppeal + AcidIndex, family = "binomial",
## data = mydata)
##
## Coefficients:
## (Intercept) FixedAcidity VolatileAcidity CitricAcid
## 7.2761837 -0.0013163 -0.2147829 0.0960032
## ResidualSugar Chlorides FreeSulfurDioxide Density
## 0.0004444 -0.1860454 0.0002738 -1.5246228
## pH Sulphates Alcohol LabelAppeal
## -0.1958777 -0.1517309 0.0007085 -0.0295854
## AcidIndex
## -0.4481867
##
## Degrees of Freedom: 9053 Total (i.e. Null); 9041 Residual
## (3623 observations deleted due to missingness)
## Null Deviance: 9319
## Residual Deviance: 8652 AIC: 8678summary(model4)##
## Call:
## glm(formula = Purchase ~ FixedAcidity + VolatileAcidity + CitricAcid +
## ResidualSugar + Chlorides + FreeSulfurDioxide + Density +
## pH + Sulphates + Alcohol + LabelAppeal + AcidIndex, family = "binomial",
## data = mydata)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.3648 0.4420 0.5696 0.6810 2.4412
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 7.2761837 1.0280751 7.077 1.47e-12 ***
## FixedAcidity -0.0013163 0.0054322 -0.242 0.808531
## VolatileAcidity -0.2147829 0.0464507 -4.624 3.77e-06 ***
## CitricAcid 0.0960032 0.0458782 2.093 0.036388 *
## ResidualSugar 0.0004444 0.0010829 0.410 0.681514
## Chlorides -0.1860454 0.1122715 -1.657 0.097499 .
## FreeSulfurDioxide 0.0002738 0.0002512 1.090 0.275711
## Density -1.5246228 1.0123853 -1.506 0.132075
## pH -0.1958777 0.0398495 -4.915 8.86e-07 ***
## Sulphates -0.1517309 0.0394776 -3.843 0.000121 ***
## Alcohol 0.0007085 0.0076481 0.093 0.926189
## LabelAppeal -0.0295854 0.0430535 -0.687 0.491971
## AcidIndex -0.4481867 0.0199514 -22.464 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 9319.1 on 9053 degrees of freedom
## Residual deviance: 8651.7 on 9041 degrees of freedom
## (3623 observations deleted due to missingness)
## AIC: 8677.7
##
## Number of Fisher Scoring iterations: 4Model5 is close to the final model. We included the STARS variable in this model, since it is allowed. The AIC has improved even more.
model5=glm(Purchase~STARS+FixedAcidity+VolatileAcidity+CitricAcid+ResidualSugar+Chlorides+FreeSulfurDioxide+Density+pH+Sulphates+Alcohol+LabelAppeal+AcidIndex,data=mydata,family="binomial")
model5##
## Call: glm(formula = Purchase ~ STARS + FixedAcidity + VolatileAcidity +
## CitricAcid + ResidualSugar + Chlorides + FreeSulfurDioxide +
## Density + pH + Sulphates + Alcohol + LabelAppeal + AcidIndex,
## family = "binomial", data = mydata)
##
## Coefficients:
## (Intercept) STARS FixedAcidity VolatileAcidity
## 3.9662770 1.9719815 0.0009698 -0.1760123
## CitricAcid ResidualSugar Chlorides FreeSulfurDioxide
## 0.0816683 0.0013079 -0.0707479 0.0003133
## Density pH Sulphates Alcohol
## -0.1662829 -0.2128037 -0.1634135 -0.0251893
## LabelAppeal AcidIndex
## 0.0867849 -0.4025495
##
## Degrees of Freedom: 9053 Total (i.e. Null); 9040 Residual
## (3623 observations deleted due to missingness)
## Null Deviance: 9319
## Residual Deviance: 5571 AIC: 5599summary(model5)##
## Call:
## glm(formula = Purchase ~ STARS + FixedAcidity + VolatileAcidity +
## CitricAcid + ResidualSugar + Chlorides + FreeSulfurDioxide +
## Density + pH + Sulphates + Alcohol + LabelAppeal + AcidIndex,
## family = "binomial", data = mydata)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.93120 0.03934 0.19291 0.49787 2.50295
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.9662770 1.2846839 3.087 0.00202 **
## STARS 1.9719815 0.0502262 39.262 < 2e-16 ***
## FixedAcidity 0.0009698 0.0069488 0.140 0.88901
## VolatileAcidity -0.1760123 0.0591098 -2.978 0.00290 **
## CitricAcid 0.0816683 0.0560160 1.458 0.14486
## ResidualSugar 0.0013079 0.0013543 0.966 0.33417
## Chlorides -0.0707479 0.1411495 -0.501 0.61621
## FreeSulfurDioxide 0.0003133 0.0003109 1.008 0.31362
## Density -0.1662829 1.2660135 -0.131 0.89550
## pH -0.2128037 0.0498256 -4.271 1.95e-05 ***
## Sulphates -0.1634135 0.0501253 -3.260 0.00111 **
## Alcohol -0.0251893 0.0095277 -2.644 0.00820 **
## LabelAppeal 0.0867849 0.0534034 1.625 0.10415
## AcidIndex -0.4025495 0.0251545 -16.003 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 9319.1 on 9053 degrees of freedom
## Residual deviance: 5570.9 on 9040 degrees of freedom
## (3623 observations deleted due to missingness)
## AIC: 5598.9
##
## Number of Fisher Scoring iterations: 6This was an analysis of how well the STARS variable does when predicting Purchased. It is one of the more powerful variables when analyzed, coming close to the AIC of model4 on its own. However, when compared via VIF values, we can see when connected with other variables it imporves theri relationsips with the Purchase variable as well:
modelSTARS=glm(Purchase~STARS, data=mydata, family='binomial')
modelSTARS##
## Call: glm(formula = Purchase ~ STARS, family = "binomial", data = mydata)
##
## Coefficients:
## (Intercept) STARS
## -0.7484 2.1816
##
## Degrees of Freedom: 12676 Total (i.e. Null); 12675 Residual
## Null Deviance: 14380
## Residual Deviance: 8473 AIC: 8477summary(modelSTARS)##
## Call:
## glm(formula = Purchase ~ STARS, family = "binomial", data = mydata)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -2.6986 -0.8802 0.2305 0.6541 1.5072
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.74840 0.03354 -22.31 <2e-16 ***
## STARS 2.18156 0.04257 51.24 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 14378.6 on 12676 degrees of freedom
## Residual deviance: 8472.9 on 12675 degrees of freedom
## AIC: 8476.9
##
## Number of Fisher Scoring iterations: 6set.seed(123)
mydata$u <- runif(n=dim(mydata)[1],min=0,max=1)
# Create train/test split;
train.df <- subset(mydata, u<0.70);
test.df <- subset(mydata, u>=0.70);
names(train.df)## [1] "Purchase" "Cases" "STARS"
## [4] "FixedAcidity" "VolatileAcidity" "CitricAcid"
## [7] "ResidualSugar" "Chlorides" "FreeSulfurDioxide"
## [10] "TotalSulfurDioxide" "Density" "pH"
## [13] "Sulphates" "Alcohol" "LabelAppeal"
## [16] "AcidIndex" "u"intmodel=glm(Purchase~1,data=train.df,family='binomial')
fullmodel=glm(Purchase~STARS+FixedAcidity+VolatileAcidity+CitricAcid+ResidualSugar+Chlorides+FreeSulfurDioxide+Density+pH+Sulphates+Alcohol+LabelAppeal+AcidIndex,data=train.df,family="binomial")library(car)## Loading required package: carDatasort(vif(fullmodel),decreasing=TRUE)## AcidIndex FixedAcidity STARS pH
## 1.070661 1.051920 1.021914 1.011627
## Alcohol LabelAppeal CitricAcid VolatileAcidity
## 1.010173 1.010026 1.004295 1.003612
## FreeSulfurDioxide ResidualSugar Chlorides Density
## 1.003531 1.003516 1.003350 1.003201
## Sulphates
## 1.002005library(car)
sort(vif(model4),decreasing=TRUE)## AcidIndex FixedAcidity pH CitricAcid
## 1.048841 1.037940 1.006466 1.003812
## Density Sulphates Alcohol Chlorides
## 1.002932 1.002468 1.002014 1.001725
## FreeSulfurDioxide ResidualSugar VolatileAcidity LabelAppeal
## 1.001158 1.001124 1.001097 1.000553In model2, we can see how the CASES and STARS variables are the most correlating. Still, we will use the fullmodel above as our predictive model, due to its best performance without the Cases variable.
sort(vif(model2),decreasing=TRUE)## STARS Cases AcidIndex LabelAppeal
## 1.207231 1.153729 1.129980 1.091676
## ResidualSugar Alcohol FixedAcidity pH
## 1.083325 1.081673 1.074755 1.054502
## CitricAcid FreeSulfurDioxide Sulphates TotalSulfurDioxide
## 1.054299 1.053398 1.043387 1.036325
## Density VolatileAcidity Chlorides
## 1.032968 1.026442 1.023629We can se our training model has a performance accuracy of around 79.2% in the table below, performin quite well.
library(rvest)
trainProb <- fullmodel %>% predict(train.df, type = "response")
trainPrediction <- ifelse(trainProb > 0.5, 1, 0)
table(train.df$Purchase, trainPrediction, dnn = c("Purchase", "Predict"))## Predict
## Purchase 0 1
## 0 822 496
## 1 467 4560Our test set model performa almost as well at 76.2% accuracy.
testProb <- fullmodel %>% predict(test.df, type = "response")
testPrediction <- ifelse(testProb > 0.5, 1, 0)
table(test.df$Purchase, testPrediction, dnn = c("Purchase", "Predict"))## Predict
## Purchase 0 1
## 0 357 231
## 1 178 1943plot(model5)
TASK 3: CONCLUSIONS AND REFLECTIONS
This assignment allowed me to sort of test what I ghave learned in this class however I wanted to. I felt most comfortable using linear models, so I decided to work on the logistic models to gain an even better understanding for it. It also seemed to be a bit simpler to work with since I would be working with binomial values. In terms of wine, I learned that the Acid levels, Alcohol content, and Label APpeal had the most influence on the purchase decision, as well as of course the amount of Stars is received. The better presented and reviewed the wine, the more likely it is to be bought. The most important parts when it comes to modeling is preprocessing the data, making sure it is usable and makes sense. Negative values for the amount of it within the wine would not make sense, so it was good to assume the absolute value of the entries, which would make a lot more sense. Next is to figure out what type of model would work best with what you are trying to predict. This was a great assignment to really test your ability on how to model data on your own.